derivation is consistent with the notion of abstract graph, i.e., any abstract derivation should start from an abstract graph and should end in an abstract graph. De nition 27 (well-de ned equivalences). For each abstract derivation [ ], de ne ([ ]) = f ( 0) j 0 2 [ ]g, and similarly ([ ]) = f ( 0) j 0 2 [ ]g. Then equivalence is well-de ned if for each derivation : G ) H we have that ([ ]) = [...

using fixed point method, we prove some new stability results for lie $(alpha,beta,gamma)$-derivations and lie $c^{ast}$-algebra homomorphisms on lie $c^{ast}$-algebras associated with the euler-lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$  is Arens regular. We also study the relationship between derivations of $A$ and $E$.

In his thesis, Remmers [R], introduced semigroup derivation diagrams and used them to prove that the word problem for finitely presented C(3) semigroups was solvable. In this article we introduce the annular analog of semigroup derivation diagrams and use them to demonstrate the solution to a conjugacy problem for finitely presented C(3) semigroups. Version of 5-21-2013

We characterize derivations and 2-local derivations from Mn(A) into Mn(M), n ≥ 2, where A is a unital algebra over C and M is a unital A-bimodule. We show that every derivation D : Mn(A) → Mn(M), n ≥ 2, is the sum of an inner derivation and a derivation induced by a derivation from A to M. We say that A commutes with M if am = ma for every a ∈ A and m ∈ M. If A commutes with M we prove that eve...

let  be a banach algebra and  a derivation. in this paper, it is proved, under certain conditions, that , where  is the jacobson radical of . moreover, we prove that if  is unital and  is a continuous derivation, then , where  denotes the set of all primitive ideals such that  is commutative,  denotes the set of all maximal (modular) ideals such that  is commutative, and  is the set of all non-...

If pi: A-->B is a surjective morphism between separable C(*)-algebras, then for each derivation delta of B there is a derivation [unk]delta of A such that pi([unk]delta(a)) for each a in A.